Reliability and validity of gain scores considered graphically

The ordinary gain score, g, is defined as g = x2-x1, where x1 is the pretest score and x2 is the posttest score. The present study extends and refines previous research on the reliability and validity of gain scores. Using particular values as stated in the tables and graphs, the pre- and posttest reliabilities, pre- and posttest validities, ratios of pretest to posttest standard deviations, and correlations between the pretest and posttest were varied systematically to examine the effects of these parameter configurations on gain scores' reliability and validity. Results plotted graphically provide insight via visual interpretation not easily inferred using only values from a table. One interesting finding was that the reliability of a gain score can be at a maximum when the validity is at a minimum. Another is that a high correlation between pre- and posttest was beneficial to the validity of the gain score but detrimental to its reliability. By identifying the situations in which gain scores can be reliable and valid, findings inform researchers when gain scores should or should not be used.